Practical prompting, backed by research

Finding: LLMs are catastrophically bad at holding implicit structure in problems with formulas. They calculate correctly but output 6.3% instead of 0.063. They confuse "independent of the variable" with "equal to zero". They wander blind even when they can do the arithmetic. The F-1 method lets you solve applied problems with formulas more accurately: financial calculations, physics, business metrics. It works in two steps inside one prompt: first the model explicitly formalizes the problem (givens → find → equations), then picks its own strategy: direct calculation, step-by-step reasoning (CoT) or code (PoT). The structure of the equations dictates how to solve. +13.3% on finance, +2.55% on physics over plain CoT.

LLMs handle short tasks fine but get lost in procedures of 20+ steps — they mix up the order, repeat what's done, forget critical checks. The problem: the model doesn't see explicit dependencies between steps and searches a huge action space at every step. PADME lets you run complex multi-step procedures (equipment diagnostics, scientific protocols, service workflows) without drift — the graph shows what follows what and where the forks are. The method separates structuring from execution: first the LLM builds a dependency graph from the text procedure (Teach phase), then walks the graph for a specific task (Execute phase). The graph is built once and reused many times with different data — the model doesn't guess what's next, it takes valid steps from the graph.